Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3398
Abstract
In this paper, we introduce two notions of closure in the category of proximity spaces which satisfy (weak) hereditariness, productivity, and idempotency, and we characterize each of $T_{i}, i=0,1,2$, proximity spaces by using these closure operators and show how these subcategories are related. Furthermore, we characterize the irreducible proximity spaces and investigate the relationship among each of irreducible, connected and $T_{i}, i=1,2$, proximity spaces. Finally, we present Tietze extension theorem and Urysohn's lemma for proximity spaces.
Keywords
Topological category, proximity space, closure operators, irreducible objects
First Page
870
Last Page
882
Recommended Citation
ÖZKAN, SAMED; KULA, MUAMMER; KULA, SÜMEYYE; and BARAN, TESNİM MERYEM
(2023)
"Closure operators, irreducibility, Urysohn's lemma, and Tietze extension theorem for proximity spaces,"
Turkish Journal of Mathematics: Vol. 47:
No.
2, Article 30.
https://doi.org/10.55730/1300-0098.3398
Available at:
https://journals.tubitak.gov.tr/math/vol47/iss2/30
